Question 1

Convert the point   to rectangular coordinates (x,y,z).

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Question 2

Using an appropriate coordinate system, evaluate the integral   where Q is the region inside the cylinder   and between the planes   and   .

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Question 3

Evaluate the iterated integral.

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Question 4

Using an appropriate coordinate system, evaluate the integral   where Q is the region inside the cylinder   and between the planes   and   .

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Question 5

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by   (includes the portion extending to z < 0) and inside the sphere defined by   .

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Question 6

Find an integral equal to the volume of the solid bounded by the given surfaces and evaluate the integral.

Accepted Answer

The answer of Find an integral equal to the volume...

Question 7

Find a constant c such that   is a joint pdf on the region bounded by   and

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Question 8

Find the surface area of the portion of   below   .

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Question 9

Find the mass of the solid with density   and the given shape.

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Question 10

Find the area of the region bounded by

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Question 11

Find the center of mass of a lamina in the shape of   , with density

Accepted Answer

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Question 12

Approximate the double integral.   , where R is bounded by x = 0, x = 1, y = 0, and y = 2x + 3

Accepted Answer

A)  1.772 
B)  0.886 
C)  2.658 
D)  2.636 
A)  1.772 
B)  0.886 
C)  2.658 
D)  2.636

Question 13

Set up and evaluate the integral   where Q is the region bounded by the coordinate planes and the planes x = 2, y = 2, and z = 2.

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Question 14

Evaluate the iterated integral by converting to polar coordinates.

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Question 15

Evaluate the iterated integral after changing coordinate systems.

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Question 16

Find the volume of the given solid Q. Q is bounded by x + z = 0, x + z = 3, -4y + 3z = 2, -4y + 3z = 3, -3y - z = -1, and -3y - z = 0.

Accepted Answer

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D)  3 
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D)  3

Question 17

Numerically estimate the surface area of the portion of   inside of

Accepted Answer

A)  3.14 
B)  5.57 
C)  116.24 
D)  114.51 
A)  3.14 
B)  5.57 
C)  116.24 
D)  114.51

Question 18

Use a double integral to find the area of the region bounded by   and   .

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Question 19

Find the Jacobian of the given transformation.

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Question 20

Change the order of integration.

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Convert the point to rectangular coordinates (x,y,z).

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Evaluate the iterated integral.

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by (includes the portion extending to z < 0) and inside the sphere defined by .

Find an integral equal to the volume of the solid bounded by the given surfaces and evaluate the integral.

Find a constant c such that is a joint pdf on the region bounded by and

Find the surface area of the portion of below .

Find the mass of the solid with density and the given shape.

Find the area of the region bounded by

Find the center of mass of a lamina in the shape of , with density

Approximate the double integral. , where R is bounded by x = 0, x = 1, y = 0, and y = 2x + 3

Set up and evaluate the integral where Q is the region bounded by the coordinate planes and the planes x = 2, y = 2, and z = 2.

Evaluate the iterated integral by converting to polar coordinates.

Evaluate the iterated integral after changing coordinate systems.

Find the volume of the given solid Q. Q is bounded by x + z = 0, x + z = 3, -4y + 3z = 2, -4y + 3z = 3, -3y - z = -1, and -3y - z = 0.

Numerically estimate the surface area of the portion of inside of

Use a double integral to find the area of the region bounded by and .

Find the Jacobian of the given transformation.

Change the order of integration.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

Filters

Exam 15: Multiple Integrals

Convert the point to rectangular coordinates (x,y,z).

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Evaluate the iterated integral.

Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Use an appropriate coordinate system to find the volume of a solid lying outside the cones defined by (includes the portion extending to z < 0) and inside the sphere defined by .

Find an integral equal to the volume of the solid bounded by the given surfaces and evaluate the integral.

Find a constant c such that is a joint pdf on the region bounded by and

Find the surface area of the portion of below .

Find the mass of the solid with density and the given shape.

Find the area of the region bounded by

Find the center of mass of a lamina in the shape of , with density

Approximate the double integral. , where R is bounded by x = 0, x = 1, y = 0, and y = 2x + 3

Set up and evaluate the integral where Q is the region bounded by the coordinate planes and the planes x = 2, y = 2, and z = 2.

Evaluate the iterated integral by converting to polar coordinates.

Evaluate the iterated integral after changing coordinate systems.

Find the volume of the given solid Q. Q is bounded by x + z = 0, x + z = 3, -4y + 3z = 2, -4y + 3z = 3, -3y - z = -1, and -3y - z = 0.

Numerically estimate the surface area of the portion of inside of

Use a double integral to find the area of the region bounded by and .

Find the Jacobian of the given transformation.

Change the order of integration.

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Vector Calculus

Second Order Differential Equations

Filters